The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0  0 X^2  0 X^2 X^2 2X^2  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 X^2 X^2  0 X^2 X^2 2X^2 X^2  0  0 X^2 X^2  0 2X^2 X^2  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0
 0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 2X^2  0  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2 2X^2  0 2X^2  0  0 X^2 X^2  0 2X^2  0 X^2 2X^2 2X^2  0 2X^2 2X^2  0  0 2X^2 X^2 X^2 X^2  0
 0  0  0 X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2 X^2  0 2X^2  0 2X^2 X^2 X^2  0 X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2  0

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+14x^108+54x^110+34x^111+486x^112+108x^113+18x^114+12x^117+2x^165

The gray image is a linear code over GF(3) with n=504, k=6 and d=324.
This code was found by Heurico 1.16 in 0.0534 seconds.